// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2016 Konstantinos Margaritis <markos@freevec.org>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
#define EIGEN_PACKET_MATH_ALTIVEC_H

namespace Eigen {

namespace internal {

#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
#endif

#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#endif

// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
#endif

    typedef __vector float Packet4f;
    typedef __vector int Packet4i;
    typedef __vector unsigned int Packet4ui;
    typedef __vector __bool int Packet4bi;
    typedef __vector short int Packet8s;
    typedef __vector unsigned short int Packet8us;
    typedef __vector signed char Packet16c;
    typedef __vector unsigned char Packet16uc;
    typedef eigen_packet_wrapper<__vector unsigned short int, 0> Packet8bf;

// We don't want to write the same code all the time, but we need to reuse the constants
// and it doesn't really work to declare them global, so we define macros instead
#define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME, X) Packet4f p4f_##NAME = {X, X, X, X}

#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME, X) Packet4i p4i_##NAME = vec_splat_s32(X)

#define _EIGEN_DECLARE_CONST_FAST_Packet4ui(NAME, X) Packet4ui p4ui_##NAME = {X, X, X, X}

#define _EIGEN_DECLARE_CONST_FAST_Packet8us(NAME, X) Packet8us p8us_##NAME = {X, X, X, X, X, X, X, X}

#define _EIGEN_DECLARE_CONST_FAST_Packet16uc(NAME, X) Packet16uc p16uc_##NAME = {X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X}

#define _EIGEN_DECLARE_CONST_Packet4f(NAME, X) Packet4f p4f_##NAME = pset1<Packet4f>(X)

#define _EIGEN_DECLARE_CONST_Packet4i(NAME, X) Packet4i p4i_##NAME = pset1<Packet4i>(X)

#define _EIGEN_DECLARE_CONST_Packet2d(NAME, X) Packet2d p2d_##NAME = pset1<Packet2d>(X)

#define _EIGEN_DECLARE_CONST_Packet2l(NAME, X) Packet2l p2l_##NAME = pset1<Packet2l>(X)

#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME, X) const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))

#define DST_CHAN 1
#define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
#define __UNPACK_TYPE__(PACKETNAME) typename unpacket_traits<PACKETNAME>::type

    // These constants are endian-agnostic
    static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0);       //{ 0.0, 0.0, 0.0, 0.0}
    static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0);       //{ 0, 0, 0, 0,}
    static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE, 1);        //{ 1, 1, 1, 1}
    static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16, -16);  //{ -16, -16, -16, -16}
    static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1, -1);    //{ -1, -1, -1, -1}
    static _EIGEN_DECLARE_CONST_FAST_Packet4ui(SIGN, 0x80000000u);
    static _EIGEN_DECLARE_CONST_FAST_Packet4ui(PREV0DOT5, 0x3EFFFFFFu);
    static _EIGEN_DECLARE_CONST_FAST_Packet8us(ONE, 1);  //{ 1, 1, 1, 1, 1, 1, 1, 1}
    static _EIGEN_DECLARE_CONST_FAST_Packet16uc(ONE, 1);
    static Packet4f p4f_MZERO = (Packet4f)vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1);  //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000}
#ifndef __VSX__
    static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0);  //{ 1.0, 1.0, 1.0, 1.0}
#endif

    static Packet4f p4f_COUNTDOWN = {0.0, 1.0, 2.0, 3.0};
    static Packet4i p4i_COUNTDOWN = {0, 1, 2, 3};
    static Packet8s p8s_COUNTDOWN = {0, 1, 2, 3, 4, 5, 6, 7};
    static Packet8us p8us_COUNTDOWN = {0, 1, 2, 3, 4, 5, 6, 7};

    static Packet16c p16c_COUNTDOWN = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
    static Packet16uc p16uc_COUNTDOWN = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};

    static Packet16uc p16uc_REVERSE32 = {12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3};
    static Packet16uc p16uc_REVERSE16 = {14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1};
    static Packet16uc p16uc_REVERSE8 = {15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0};

    static Packet16uc p16uc_DUPLICATE32_HI = {0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7};
    static Packet16uc p16uc_DUPLICATE16_HI = {0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7};
    static Packet16uc p16uc_DUPLICATE8_HI = {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7};
    static const Packet16uc p16uc_DUPLICATE16_EVEN = {0, 1, 0, 1, 4, 5, 4, 5, 8, 9, 8, 9, 12, 13, 12, 13};
    static const Packet16uc p16uc_DUPLICATE16_ODD = {2, 3, 2, 3, 6, 7, 6, 7, 10, 11, 10, 11, 14, 15, 14, 15};

    static Packet16uc p16uc_QUADRUPLICATE16_HI = {0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3};

// Handle endianness properly while loading constants
// Define global static constants:
#ifdef _BIG_ENDIAN
    static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
#ifdef __VSX__
    static Packet16uc p16uc_REVERSE64 = {8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7};
#endif
    static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 0),
                                                  (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 2),
                                                  8);  //{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
    static Packet16uc p16uc_PSET32_WEVEN =
        vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);  //{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
    static Packet16uc p16uc_HALF64_0_16 =
        vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc)vec_abs(p4i_MINUS16), 3), 8);  //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
#else
    static Packet16uc p16uc_FORWARD = p16uc_REVERSE32;
    static Packet16uc p16uc_REVERSE64 = {8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7};
    static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 1),
                                                  (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 3),
                                                  8);  //{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
    static Packet16uc p16uc_PSET32_WEVEN = vec_sld((Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 0),
                                                   (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 2),
                                                   8);  //{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
    static Packet16uc p16uc_HALF64_0_16 =
        vec_sld(vec_splat((Packet16uc)vec_abs(p4i_MINUS16), 0), (Packet16uc)p4i_ZERO, 8);   //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
#endif  // _BIG_ENDIAN

    static Packet16uc p16uc_PSET64_HI =
        (Packet16uc)vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);  //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
    static Packet16uc p16uc_PSET64_LO =
        (Packet16uc)vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);  //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
    static Packet16uc p16uc_TRANSPOSE64_HI = p16uc_PSET64_HI + p16uc_HALF64_0_16;             //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
    static Packet16uc p16uc_TRANSPOSE64_LO = p16uc_PSET64_LO + p16uc_HALF64_0_16;             //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};

    static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);  //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };

#ifdef _BIG_ENDIAN
    static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);  //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
#else
    static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_PSET64_HI, p16uc_PSET64_LO, 8);  //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
#endif  // _BIG_ENDIAN

#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
#define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR);
#else
#define EIGEN_PPC_PREFETCH(ADDR) asm("   dcbt [%[addr]]\n" ::[addr] "r"(ADDR) : "cc");
#endif

    template <> struct packet_traits<float> : default_packet_traits
    {
        typedef Packet4f type;
        typedef Packet4f half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 4,
            HasHalfPacket = 1,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 1,
            HasMin = 1,
            HasMax = 1,
            HasAbs = 1,
            HasSin = EIGEN_FAST_MATH,
            HasCos = EIGEN_FAST_MATH,
            HasLog = 1,
            HasExp = 1,
#ifdef __VSX__
            HasSqrt = 1,
#if !EIGEN_COMP_CLANG
            HasRsqrt = 1,
#else
            HasRsqrt = 0,
#endif
#else
            HasSqrt = 0,
            HasRsqrt = 0,
            HasTanh = EIGEN_FAST_MATH,
            HasErf = EIGEN_FAST_MATH,
#endif
            HasRound = 1,
            HasFloor = 1,
            HasCeil = 1,
            HasRint = 1,
            HasNegate = 1,
            HasBlend = 1
        };
    };
    template <> struct packet_traits<bfloat16> : default_packet_traits
    {
        typedef Packet8bf type;
        typedef Packet8bf half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 8,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 1,
            HasMin = 1,
            HasMax = 1,
            HasAbs = 1,
            HasSin = EIGEN_FAST_MATH,
            HasCos = EIGEN_FAST_MATH,
            HasLog = 1,
            HasExp = 1,
#ifdef __VSX__
            HasSqrt = 1,
#if !EIGEN_COMP_CLANG
            HasRsqrt = 1,
#else
            HasRsqrt = 0,
#endif
#else
            HasSqrt = 0,
            HasRsqrt = 0,
            HasTanh = EIGEN_FAST_MATH,
            HasErf = EIGEN_FAST_MATH,
#endif
            HasRound = 1,
            HasFloor = 1,
            HasCeil = 1,
            HasRint = 1,
            HasNegate = 1,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<int> : default_packet_traits
    {
        typedef Packet4i type;
        typedef Packet4i half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 4,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasShift = 1,
            HasMul = 1,
            HasDiv = 0,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<short int> : default_packet_traits
    {
        typedef Packet8s type;
        typedef Packet8s half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 8,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 0,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<unsigned short int> : default_packet_traits
    {
        typedef Packet8us type;
        typedef Packet8us half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 8,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 0,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<signed char> : default_packet_traits
    {
        typedef Packet16c type;
        typedef Packet16c half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 16,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 0,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<unsigned char> : default_packet_traits
    {
        typedef Packet16uc type;
        typedef Packet16uc half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 16,
            HasHalfPacket = 0,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 0,
            HasBlend = 1
        };
    };

    template <> struct unpacket_traits<Packet4f>
    {
        typedef float type;
        typedef Packet4f half;
        typedef Packet4i integer_packet;
        enum
        {
            size = 4,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet4i>
    {
        typedef int type;
        typedef Packet4i half;
        enum
        {
            size = 4,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet8s>
    {
        typedef short int type;
        typedef Packet8s half;
        enum
        {
            size = 8,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet8us>
    {
        typedef unsigned short int type;
        typedef Packet8us half;
        enum
        {
            size = 8,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };

    template <> struct unpacket_traits<Packet16c>
    {
        typedef signed char type;
        typedef Packet16c half;
        enum
        {
            size = 16,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet16uc>
    {
        typedef unsigned char type;
        typedef Packet16uc half;
        enum
        {
            size = 16,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };

    template <> struct unpacket_traits<Packet8bf>
    {
        typedef bfloat16 type;
        typedef Packet8bf half;
        enum
        {
            size = 8,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    inline std::ostream& operator<<(std::ostream& s, const Packet16c& v)
    {
        union
        {
            Packet16c v;
            signed char n[16];
        } vt;
        vt.v = v;
        for (int i = 0; i < 16; i++) s << vt.n[i] << ", ";
        return s;
    }

    inline std::ostream& operator<<(std::ostream& s, const Packet16uc& v)
    {
        union
        {
            Packet16uc v;
            unsigned char n[16];
        } vt;
        vt.v = v;
        for (int i = 0; i < 16; i++) s << vt.n[i] << ", ";
        return s;
    }

    inline std::ostream& operator<<(std::ostream& s, const Packet4f& v)
    {
        union
        {
            Packet4f v;
            float n[4];
        } vt;
        vt.v = v;
        s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
        return s;
    }

    inline std::ostream& operator<<(std::ostream& s, const Packet4i& v)
    {
        union
        {
            Packet4i v;
            int n[4];
        } vt;
        vt.v = v;
        s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
        return s;
    }

    inline std::ostream& operator<<(std::ostream& s, const Packet4ui& v)
    {
        union
        {
            Packet4ui v;
            unsigned int n[4];
        } vt;
        vt.v = v;
        s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
        return s;
    }

    template <typename Packet> EIGEN_STRONG_INLINE Packet pload_common(const __UNPACK_TYPE__(Packet) * from)
    {
        // some versions of GCC throw "unused-but-set-parameter".
        // ignoring these warnings for now.
        EIGEN_UNUSED_VARIABLE(from);
        EIGEN_DEBUG_ALIGNED_LOAD
#ifdef __VSX__
        return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
#else
        return vec_ld(0, from);
#endif
    }

    // Need to define them first or we get specialization after instantiation errors
    template <> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { return pload_common<Packet4f>(from); }

    template <> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { return pload_common<Packet4i>(from); }

    template <> EIGEN_STRONG_INLINE Packet8s pload<Packet8s>(const short int* from) { return pload_common<Packet8s>(from); }

    template <> EIGEN_STRONG_INLINE Packet8us pload<Packet8us>(const unsigned short int* from) { return pload_common<Packet8us>(from); }

    template <> EIGEN_STRONG_INLINE Packet16c pload<Packet16c>(const signed char* from) { return pload_common<Packet16c>(from); }

    template <> EIGEN_STRONG_INLINE Packet16uc pload<Packet16uc>(const unsigned char* from) { return pload_common<Packet16uc>(from); }

    template <> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16* from)
    {
        return pload_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
    }

    template <typename Packet> EIGEN_STRONG_INLINE void pstore_common(__UNPACK_TYPE__(Packet) * to, const Packet& from)
    {
        // some versions of GCC throw "unused-but-set-parameter" (float *to).
        // ignoring these warnings for now.
        EIGEN_UNUSED_VARIABLE(to);
        EIGEN_DEBUG_ALIGNED_STORE
#ifdef __VSX__
        vec_xst(from, 0, to);
#else
        vec_st(from, 0, to);
#endif
    }

    template <> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { pstore_common<Packet4f>(to, from); }

    template <> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { pstore_common<Packet4i>(to, from); }

    template <> EIGEN_STRONG_INLINE void pstore<short int>(short int* to, const Packet8s& from) { pstore_common<Packet8s>(to, from); }

    template <> EIGEN_STRONG_INLINE void pstore<unsigned short int>(unsigned short int* to, const Packet8us& from) { pstore_common<Packet8us>(to, from); }

    template <> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet8bf& from)
    {
        pstore_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
    }

    template <> EIGEN_STRONG_INLINE void pstore<signed char>(signed char* to, const Packet16c& from) { pstore_common<Packet16c>(to, from); }

    template <> EIGEN_STRONG_INLINE void pstore<unsigned char>(unsigned char* to, const Packet16uc& from) { pstore_common<Packet16uc>(to, from); }

    template <typename Packet> EIGEN_STRONG_INLINE Packet pset1_size4(const __UNPACK_TYPE__(Packet) & from)
    {
        Packet v = {from, from, from, from};
        return v;
    }

    template <typename Packet> EIGEN_STRONG_INLINE Packet pset1_size8(const __UNPACK_TYPE__(Packet) & from)
    {
        Packet v = {from, from, from, from, from, from, from, from};
        return v;
    }

    template <typename Packet> EIGEN_STRONG_INLINE Packet pset1_size16(const __UNPACK_TYPE__(Packet) & from)
    {
        Packet v = {from, from, from, from, from, from, from, from, from, from, from, from, from, from, from, from};
        return v;
    }

    template <> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return pset1_size4<Packet4f>(from); }

    template <> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return pset1_size4<Packet4i>(from); }

    template <> EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const short int& from) { return pset1_size8<Packet8s>(from); }

    template <> EIGEN_STRONG_INLINE Packet8us pset1<Packet8us>(const unsigned short int& from) { return pset1_size8<Packet8us>(from); }

    template <> EIGEN_STRONG_INLINE Packet16c pset1<Packet16c>(const signed char& from) { return pset1_size16<Packet16c>(from); }

    template <> EIGEN_STRONG_INLINE Packet16uc pset1<Packet16uc>(const unsigned char& from) { return pset1_size16<Packet16uc>(from); }

    template <> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return reinterpret_cast<Packet4f>(pset1<Packet4i>(from)); }

    template <> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16& from)
    {
        return pset1_size8<Packet8us>(reinterpret_cast<const unsigned short int&>(from));
    }

    template <typename Packet> EIGEN_STRONG_INLINE void pbroadcast4_common(const __UNPACK_TYPE__(Packet) * a, Packet& a0, Packet& a1, Packet& a2, Packet& a3)
    {
        a3 = pload<Packet>(a);
        a0 = vec_splat(a3, 0);
        a1 = vec_splat(a3, 1);
        a2 = vec_splat(a3, 2);
        a3 = vec_splat(a3, 3);
    }

    template <> EIGEN_STRONG_INLINE void pbroadcast4<Packet4f>(const float* a, Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
    {
        pbroadcast4_common<Packet4f>(a, a0, a1, a2, a3);
    }
    template <> EIGEN_STRONG_INLINE void pbroadcast4<Packet4i>(const int* a, Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
    {
        pbroadcast4_common<Packet4i>(a, a0, a1, a2, a3);
    }

    template <typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_common(const __UNPACK_TYPE__(Packet) * from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[4];
        a[0] = from[0 * stride];
        a[1] = from[1 * stride];
        a[2] = from[2 * stride];
        a[3] = from[3 * stride];
        return pload<Packet>(a);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride) { return pgather_common<Packet4f>(from, stride); }

    template <> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride) { return pgather_common<Packet4i>(from, stride); }

    template <typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_size8(const __UNPACK_TYPE__(Packet) * from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[8];
        a[0] = from[0 * stride];
        a[1] = from[1 * stride];
        a[2] = from[2 * stride];
        a[3] = from[3 * stride];
        a[4] = from[4 * stride];
        a[5] = from[5 * stride];
        a[6] = from[6 * stride];
        a[7] = from[7 * stride];
        return pload<Packet>(a);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet8s pgather<short int, Packet8s>(const short int* from, Index stride)
    {
        return pgather_size8<Packet8s>(from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet8us pgather<unsigned short int, Packet8us>(const unsigned short int* from, Index stride)
    {
        return pgather_size8<Packet8us>(from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet8bf pgather<bfloat16, Packet8bf>(const bfloat16* from, Index stride)
    {
        return pgather_size8<Packet8bf>(from, stride);
    }

    template <typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_size16(const __UNPACK_TYPE__(Packet) * from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[16];
        a[0] = from[0 * stride];
        a[1] = from[1 * stride];
        a[2] = from[2 * stride];
        a[3] = from[3 * stride];
        a[4] = from[4 * stride];
        a[5] = from[5 * stride];
        a[6] = from[6 * stride];
        a[7] = from[7 * stride];
        a[8] = from[8 * stride];
        a[9] = from[9 * stride];
        a[10] = from[10 * stride];
        a[11] = from[11 * stride];
        a[12] = from[12 * stride];
        a[13] = from[13 * stride];
        a[14] = from[14 * stride];
        a[15] = from[15 * stride];
        return pload<Packet>(a);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet16c pgather<signed char, Packet16c>(const signed char* from, Index stride)
    {
        return pgather_size16<Packet16c>(from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet16uc pgather<unsigned char, Packet16uc>(const unsigned char* from, Index stride)
    {
        return pgather_size16<Packet16uc>(from, stride);
    }

    template <typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size4(__UNPACK_TYPE__(Packet) * to, const Packet& from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[4];
        pstore<__UNPACK_TYPE__(Packet)>(a, from);
        to[0 * stride] = a[0];
        to[1 * stride] = a[1];
        to[2 * stride] = a[2];
        to[3 * stride] = a[3];
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
    {
        pscatter_size4<Packet4f>(to, from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
    {
        pscatter_size4<Packet4i>(to, from, stride);
    }

    template <typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size8(__UNPACK_TYPE__(Packet) * to, const Packet& from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[8];
        pstore<__UNPACK_TYPE__(Packet)>(a, from);
        to[0 * stride] = a[0];
        to[1 * stride] = a[1];
        to[2 * stride] = a[2];
        to[3 * stride] = a[3];
        to[4 * stride] = a[4];
        to[5 * stride] = a[5];
        to[6 * stride] = a[6];
        to[7 * stride] = a[7];
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<short int, Packet8s>(short int* to, const Packet8s& from, Index stride)
    {
        pscatter_size8<Packet8s>(to, from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<unsigned short int, Packet8us>(unsigned short int* to, const Packet8us& from, Index stride)
    {
        pscatter_size8<Packet8us>(to, from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride)
    {
        pscatter_size8<Packet8bf>(to, from, stride);
    }

    template <typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size16(__UNPACK_TYPE__(Packet) * to, const Packet& from, Index stride)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[16];
        pstore<__UNPACK_TYPE__(Packet)>(a, from);
        to[0 * stride] = a[0];
        to[1 * stride] = a[1];
        to[2 * stride] = a[2];
        to[3 * stride] = a[3];
        to[4 * stride] = a[4];
        to[5 * stride] = a[5];
        to[6 * stride] = a[6];
        to[7 * stride] = a[7];
        to[8 * stride] = a[8];
        to[9 * stride] = a[9];
        to[10 * stride] = a[10];
        to[11 * stride] = a[11];
        to[12 * stride] = a[12];
        to[13 * stride] = a[13];
        to[14 * stride] = a[14];
        to[15 * stride] = a[15];
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<signed char, Packet16c>(signed char* to, const Packet16c& from, Index stride)
    {
        pscatter_size16<Packet16c>(to, from, stride);
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<unsigned char, Packet16uc>(unsigned char* to, const Packet16uc& from, Index stride)
    {
        pscatter_size16<Packet16uc>(to, from, stride);
    }

    template <> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; }
    template <> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return pset1<Packet4i>(a) + p4i_COUNTDOWN; }
    template <> EIGEN_STRONG_INLINE Packet8s plset<Packet8s>(const short int& a) { return pset1<Packet8s>(a) + p8s_COUNTDOWN; }
    template <> EIGEN_STRONG_INLINE Packet8us plset<Packet8us>(const unsigned short int& a) { return pset1<Packet8us>(a) + p8us_COUNTDOWN; }
    template <> EIGEN_STRONG_INLINE Packet16c plset<Packet16c>(const signed char& a) { return pset1<Packet16c>(a) + p16c_COUNTDOWN; }
    template <> EIGEN_STRONG_INLINE Packet16uc plset<Packet16uc>(const unsigned char& a) { return pset1<Packet16uc>(a) + p16uc_COUNTDOWN; }

    template <> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet4ui padd<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet8s padd<Packet8s>(const Packet8s& a, const Packet8s& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet8us padd<Packet8us>(const Packet8us& a, const Packet8us& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet16c padd<Packet16c>(const Packet16c& a, const Packet16c& b) { return a + b; }
    template <> EIGEN_STRONG_INLINE Packet16uc padd<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return a + b; }

    template <> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return a - b; }
    template <> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return a - b; }
    template <> EIGEN_STRONG_INLINE Packet8s psub<Packet8s>(const Packet8s& a, const Packet8s& b) { return a - b; }
    template <> EIGEN_STRONG_INLINE Packet8us psub<Packet8us>(const Packet8us& a, const Packet8us& b) { return a - b; }
    template <> EIGEN_STRONG_INLINE Packet16c psub<Packet16c>(const Packet16c& a, const Packet16c& b) { return a - b; }
    template <> EIGEN_STRONG_INLINE Packet16uc psub<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return a - b; }

    template <> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return p4f_ZERO - a; }
    template <> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return p4i_ZERO - a; }

    template <> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
    template <> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }

    template <> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a, b, p4f_MZERO); }
    template <> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return a * b; }
    template <> EIGEN_STRONG_INLINE Packet8s pmul<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_mul(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8us pmul<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_mul(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16c pmul<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_mul(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_mul(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#ifndef __VSX__  // VSX actually provides a div instruction
        Packet4f t, y_0, y_1;

        // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
        y_0 = vec_re(b);

        // Do one Newton-Raphson iteration to get the needed accuracy
        t = vec_nmsub(y_0, b, p4f_ONE);
        y_1 = vec_madd(y_0, t, y_0);

        return vec_madd(a, y_1, p4f_MZERO);
#else
        return vec_div(a, b);
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
    {
        eigen_assert(false && "packet integer division are not supported by AltiVec");
        return pset1<Packet4i>(0);
    }

    // for some weird raisons, it has to be overloaded for packet of integers
    template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
    template <> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a * b + c; }
    template <> EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c) { return vec_madd(a, b, c); }
    template <> EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c) { return vec_madd(a, b, c); }

    template <> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#ifdef __VSX__
        // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
        Packet4f ret;
        __asm__("xvcmpgesp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa"(ret) : "wa"(a), "wa"(b));
        return ret;
#else
        return vec_min(a, b);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8s pmin<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_min(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8us pmin<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_min(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_min(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_min(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#ifdef __VSX__
        // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
        Packet4f ret;
        __asm__("xvcmpgtsp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa"(ret) : "wa"(a), "wa"(b));
        return ret;
#else
        return vec_max(a, b);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8s pmax<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_max(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8us pmax<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_max(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16c pmax<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_max(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16uc pmax<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_max(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b)
    {
        Packet4f c = reinterpret_cast<Packet4f>(vec_cmpge(a, b));
        return vec_nor(c, c);
    }

    template <> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8s pcmp_le(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8s pcmp_lt(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8s pcmp_eq(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8us pcmp_le(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8us pcmp_lt(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet8us pcmp_eq(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16c pcmp_le(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16c pcmp_lt(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16c pcmp_eq(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16uc pcmp_le(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16uc pcmp_lt(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet16uc pcmp_eq(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmpeq(a, b)); }

    template <> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vec_and(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_and(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8bf pand<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { return pand<Packet8us>(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_or(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_or(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8bf por<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { return por<Packet8us>(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
    template <> EIGEN_STRONG_INLINE Packet8bf pxor<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { return pxor<Packet8us>(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_andc(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_andc(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b)
    {
        return vec_sel(b, a, reinterpret_cast<Packet4ui>(mask));
    }

    template <> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
    {
        Packet4f t = vec_add(reinterpret_cast<Packet4f>(vec_or(vec_and(reinterpret_cast<Packet4ui>(a), p4ui_SIGN), p4ui_PREV0DOT5)), a);
        Packet4f res;

#ifdef __VSX__
        __asm__("xvrspiz %x0, %x1\n\t" : "=&wa"(res) : "wa"(t));
#else
        __asm__("vrfiz %0, %1\n\t" : "=v"(res) : "v"(t));
#endif

        return res;
    }
    template <> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return vec_ceil(a); }
    template <> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
    template <> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
    {
        Packet4f res;

        __asm__("xvrspic %x0, %x1\n\t" : "=&wa"(res) : "wa"(a));

        return res;
    }

    template <typename Packet> EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet) * from)
    {
        EIGEN_DEBUG_ALIGNED_LOAD
#ifdef _BIG_ENDIAN
        Packet16uc MSQ, LSQ;
        Packet16uc mask;
        MSQ = vec_ld(0, (unsigned char*)from);   // most significant quadword
        LSQ = vec_ld(15, (unsigned char*)from);  // least significant quadword
        mask = vec_lvsl(0, from);                // create the permute mask
        //TODO: Add static_cast here
        return (Packet)vec_perm(MSQ, LSQ, mask);  // align the data
#else
        EIGEN_DEBUG_UNALIGNED_LOAD
        return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { return ploadu_common<Packet4f>(from); }
    template <> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { return ploadu_common<Packet4i>(from); }
    template <> EIGEN_STRONG_INLINE Packet8s ploadu<Packet8s>(const short int* from) { return ploadu_common<Packet8s>(from); }
    template <> EIGEN_STRONG_INLINE Packet8us ploadu<Packet8us>(const unsigned short int* from) { return ploadu_common<Packet8us>(from); }
    template <> EIGEN_STRONG_INLINE Packet8bf ploadu<Packet8bf>(const bfloat16* from)
    {
        return ploadu_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
    }
    template <> EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const signed char* from) { return ploadu_common<Packet16c>(from); }
    template <> EIGEN_STRONG_INLINE Packet16uc ploadu<Packet16uc>(const unsigned char* from) { return ploadu_common<Packet16uc>(from); }

    template <typename Packet> EIGEN_STRONG_INLINE Packet ploaddup_common(const __UNPACK_TYPE__(Packet) * from)
    {
        Packet p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet>(from);
        else
            p = ploadu<Packet>(from);
        return vec_perm(p, p, p16uc_DUPLICATE32_HI);
    }
    template <> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from) { return ploaddup_common<Packet4f>(from); }
    template <> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from) { return ploaddup_common<Packet4i>(from); }

    template <> EIGEN_STRONG_INLINE Packet8s ploaddup<Packet8s>(const short int* from)
    {
        Packet8s p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet8s>(from);
        else
            p = ploadu<Packet8s>(from);
        return vec_perm(p, p, p16uc_DUPLICATE16_HI);
    }

    template <> EIGEN_STRONG_INLINE Packet8us ploaddup<Packet8us>(const unsigned short int* from)
    {
        Packet8us p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet8us>(from);
        else
            p = ploadu<Packet8us>(from);
        return vec_perm(p, p, p16uc_DUPLICATE16_HI);
    }

    template <> EIGEN_STRONG_INLINE Packet8s ploadquad<Packet8s>(const short int* from)
    {
        Packet8s p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet8s>(from);
        else
            p = ploadu<Packet8s>(from);
        return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
    }

    template <> EIGEN_STRONG_INLINE Packet8us ploadquad<Packet8us>(const unsigned short int* from)
    {
        Packet8us p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet8us>(from);
        else
            p = ploadu<Packet8us>(from);
        return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
    }

    template <> EIGEN_STRONG_INLINE Packet8bf ploadquad<Packet8bf>(const bfloat16* from)
    {
        return ploadquad<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
    }

    template <> EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const signed char* from)
    {
        Packet16c p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet16c>(from);
        else
            p = ploadu<Packet16c>(from);
        return vec_perm(p, p, p16uc_DUPLICATE8_HI);
    }

    template <> EIGEN_STRONG_INLINE Packet16uc ploaddup<Packet16uc>(const unsigned char* from)
    {
        Packet16uc p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet16uc>(from);
        else
            p = ploadu<Packet16uc>(from);
        return vec_perm(p, p, p16uc_DUPLICATE8_HI);
    }

    template <typename Packet> EIGEN_STRONG_INLINE void pstoreu_common(__UNPACK_TYPE__(Packet) * to, const Packet& from)
    {
        EIGEN_DEBUG_UNALIGNED_STORE
#ifdef _BIG_ENDIAN
        // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
        // Warning: not thread safe!
        Packet16uc MSQ, LSQ, edges;
        Packet16uc edgeAlign, align;

        MSQ = vec_ld(0, (unsigned char*)to);             // most significant quadword
        LSQ = vec_ld(15, (unsigned char*)to);            // least significant quadword
        edgeAlign = vec_lvsl(0, to);                     // permute map to extract edges
        edges = vec_perm(LSQ, MSQ, edgeAlign);           // extract the edges
        align = vec_lvsr(0, to);                         // permute map to misalign data
        MSQ = vec_perm(edges, (Packet16uc)from, align);  // misalign the data (MSQ)
        LSQ = vec_perm((Packet16uc)from, edges, align);  // misalign the data (LSQ)
        vec_st(LSQ, 15, (unsigned char*)to);             // Store the LSQ part first
        vec_st(MSQ, 0, (unsigned char*)to);              // Store the MSQ part second
#else
        vec_xst(from, 0, to);
#endif
    }
    template <> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { pstoreu_common<Packet4f>(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { pstoreu_common<Packet4i>(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<short int>(short int* to, const Packet8s& from) { pstoreu_common<Packet8s>(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<unsigned short int>(unsigned short int* to, const Packet8us& from) { pstoreu_common<Packet8us>(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet8bf& from)
    {
        pstoreu_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
    }
    template <> EIGEN_STRONG_INLINE void pstoreu<signed char>(signed char* to, const Packet16c& from) { pstoreu_common<Packet16c>(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<unsigned char>(unsigned char* to, const Packet16uc& from) { pstoreu_common<Packet16uc>(to, from); }

    template <> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_PPC_PREFETCH(addr); }
    template <> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_PPC_PREFETCH(addr); }

    template <> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a)
    {
        EIGEN_ALIGN16 float x;
        vec_ste(a, 0, &x);
        return x;
    }
    template <> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a)
    {
        EIGEN_ALIGN16 int x;
        vec_ste(a, 0, &x);
        return x;
    }

    template <typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) pfirst_common(const Packet& a)
    {
        EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) x;
        vec_ste(a, 0, &x);
        return x;
    }

    template <> EIGEN_STRONG_INLINE short int pfirst<Packet8s>(const Packet8s& a) { return pfirst_common<Packet8s>(a); }

    template <> EIGEN_STRONG_INLINE unsigned short int pfirst<Packet8us>(const Packet8us& a) { return pfirst_common<Packet8us>(a); }

    template <> EIGEN_STRONG_INLINE signed char pfirst<Packet16c>(const Packet16c& a) { return pfirst_common<Packet16c>(a); }

    template <> EIGEN_STRONG_INLINE unsigned char pfirst<Packet16uc>(const Packet16uc& a) { return pfirst_common<Packet16uc>(a); }

    template <> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
    {
        return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
    }
    template <> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
    {
        return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
    }
    template <> EIGEN_STRONG_INLINE Packet8s preverse(const Packet8s& a)
    {
        return reinterpret_cast<Packet8s>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
    }
    template <> EIGEN_STRONG_INLINE Packet8us preverse(const Packet8us& a)
    {
        return reinterpret_cast<Packet8us>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
    }
    template <> EIGEN_STRONG_INLINE Packet16c preverse(const Packet16c& a) { return vec_perm(a, a, p16uc_REVERSE8); }
    template <> EIGEN_STRONG_INLINE Packet16uc preverse(const Packet16uc& a) { return vec_perm(a, a, p16uc_REVERSE8); }
    template <> EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a) { return preverse<Packet8us>(a); }

    template <> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
    template <> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
    template <> EIGEN_STRONG_INLINE Packet8s pabs(const Packet8s& a) { return vec_abs(a); }
    template <> EIGEN_STRONG_INLINE Packet8us pabs(const Packet8us& a) { return a; }
    template <> EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) { return vec_abs(a); }
    template <> EIGEN_STRONG_INLINE Packet16uc pabs(const Packet16uc& a) { return a; }
    template <> EIGEN_STRONG_INLINE Packet8bf pabs(const Packet8bf& a)
    {
        _EIGEN_DECLARE_CONST_FAST_Packet8us(abs_mask, 0x7FFF);
        return pand<Packet8us>(p8us_abs_mask, a);
    }

    template <int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a)
    {
        return vec_sra(a, reinterpret_cast<Packet4ui>(pset1<Packet4i>(N)));
    }
    template <int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a) { return vec_sr(a, reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
    template <int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a) { return vec_sl(a, reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
    template <int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_left(const Packet4f& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
        Packet4ui r = vec_sl(reinterpret_cast<Packet4ui>(a), p4ui_mask);
        return reinterpret_cast<Packet4f>(r);
    }

    template <int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_right(const Packet4f& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
        Packet4ui r = vec_sr(reinterpret_cast<Packet4ui>(a), p4ui_mask);
        return reinterpret_cast<Packet4f>(r);
    }

    template <int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(const Packet4ui& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
        return vec_sr(a, p4ui_mask);
    }

    template <int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(const Packet4ui& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
        return vec_sl(a, p4ui_mask);
    }

    template <int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_left(const Packet8us& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
        return vec_sl(a, p8us_mask);
    }
    template <int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_right(const Packet8us& a)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
        return vec_sr(a, p8us_mask);
    }

    EIGEN_STRONG_INLINE Packet4f Bf16ToF32Even(const Packet8bf& bf) { return plogical_shift_left<16>(reinterpret_cast<Packet4f>(bf.m_val)); }

    EIGEN_STRONG_INLINE Packet4f Bf16ToF32Odd(const Packet8bf& bf)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
        return pand<Packet4f>(reinterpret_cast<Packet4f>(bf.m_val), reinterpret_cast<Packet4f>(p4ui_high_mask));
    }

    // Simple interleaving of bool masks, prevents true values from being
    // converted to NaNs.
    EIGEN_STRONG_INLINE Packet8bf F32ToBf16Bool(Packet4f even, Packet4f odd)
    {
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
        Packet4f bf_odd, bf_even;
        bf_odd = pand(reinterpret_cast<Packet4f>(p4ui_high_mask), odd);
        bf_even = plogical_shift_right<16>(even);
        return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
    }

    EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f)
    {
        Packet4ui input = reinterpret_cast<Packet4ui>(p4f);
        Packet4ui lsb = plogical_shift_right<16>(input);
        lsb = pand<Packet4ui>(lsb, reinterpret_cast<Packet4ui>(p4i_ONE));

        _EIGEN_DECLARE_CONST_FAST_Packet4ui(BIAS, 0x7FFFu);
        Packet4ui rounding_bias = padd<Packet4ui>(lsb, p4ui_BIAS);
        input = padd<Packet4ui>(input, rounding_bias);

        //Test NaN and Subnormal - Begin
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(exp_mask, 0x7F800000);
        Packet4ui exp = pand<Packet4ui>(p4ui_exp_mask, reinterpret_cast<Packet4ui>(p4f));

        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mantissa_mask, 0x7FFFFF);
        Packet4ui mantissa = pand<Packet4ui>(p4ui_mantissa_mask, reinterpret_cast<Packet4ui>(p4f));

        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(max_exp, 0x7F800000);
        Packet4bi is_max_exp = vec_cmpeq(exp, p4ui_max_exp);
        Packet4bi is_zero_exp = vec_cmpeq(exp, reinterpret_cast<Packet4ui>(p4i_ZERO));

        Packet4bi is_mant_zero = vec_cmpeq(mantissa, reinterpret_cast<Packet4ui>(p4i_ZERO));
        Packet4ui nan_selector = pandnot<Packet4ui>(reinterpret_cast<Packet4ui>(is_max_exp), reinterpret_cast<Packet4ui>(is_mant_zero));

        Packet4ui subnormal_selector = pandnot<Packet4ui>(reinterpret_cast<Packet4ui>(is_zero_exp), reinterpret_cast<Packet4ui>(is_mant_zero));

        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(nan, 0x7FC00000);
        input = vec_sel(input, p4ui_nan, nan_selector);
        input = vec_sel(input, reinterpret_cast<Packet4ui>(p4f), subnormal_selector);
        //Test NaN and Subnormal - End

        input = plogical_shift_right<16>(input);
        return reinterpret_cast<Packet8us>(input);
    }

    EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f even, Packet4f odd)
    {
        Packet4f bf_odd, bf_even;
        bf_odd = reinterpret_cast<Packet4f>(F32ToBf16(odd).m_val);
        bf_odd = plogical_shift_left<16>(bf_odd);
        bf_even = reinterpret_cast<Packet4f>(F32ToBf16(even).m_val);
        return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
    }
#define BF16_TO_F32_UNARY_OP_WRAPPER(OP, A) \
    Packet4f a_even = Bf16ToF32Even(A);     \
    Packet4f a_odd = Bf16ToF32Odd(A);       \
    Packet4f op_even = OP(a_even);          \
    Packet4f op_odd = OP(a_odd);            \
    return F32ToBf16(op_even, op_odd);

#define BF16_TO_F32_BINARY_OP_WRAPPER(OP, A, B) \
    Packet4f a_even = Bf16ToF32Even(A);         \
    Packet4f a_odd = Bf16ToF32Odd(A);           \
    Packet4f b_even = Bf16ToF32Even(B);         \
    Packet4f b_odd = Bf16ToF32Odd(B);           \
    Packet4f op_even = OP(a_even, b_even);      \
    Packet4f op_odd = OP(a_odd, b_odd);         \
    return F32ToBf16(op_even, op_odd);

#define BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(OP, A, B) \
    Packet4f a_even = Bf16ToF32Even(A);              \
    Packet4f a_odd = Bf16ToF32Odd(A);                \
    Packet4f b_even = Bf16ToF32Even(B);              \
    Packet4f b_odd = Bf16ToF32Odd(B);                \
    Packet4f op_even = OP(a_even, b_even);           \
    Packet4f op_odd = OP(a_odd, b_odd);              \
    return F32ToBf16Bool(op_even, op_odd);

    template <> EIGEN_STRONG_INLINE Packet8bf padd<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(padd<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(pmul<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(pdiv<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf pnegate<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pnegate<Packet4f>, a); }

    template <> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(psub<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(vec_sqrt, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a); }

    template <> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) { return pldexp_generic(a, exponent); }
    template <> EIGEN_STRONG_INLINE Packet8bf pldexp<Packet8bf>(const Packet8bf& a, const Packet8bf& exponent)
    {
        BF16_TO_F32_BINARY_OP_WRAPPER(pldexp<Packet4f>, a, exponent);
    }

    template <> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) { return pfrexp_generic(a, exponent); }
    template <> EIGEN_STRONG_INLINE Packet8bf pfrexp<Packet8bf>(const Packet8bf& a, Packet8bf& e)
    {
        Packet4f a_even = Bf16ToF32Even(a);
        Packet4f a_odd = Bf16ToF32Odd(a);
        Packet4f e_even;
        Packet4f e_odd;
        Packet4f op_even = pfrexp<Packet4f>(a_even, e_even);
        Packet4f op_odd = pfrexp<Packet4f>(a_odd, e_odd);
        e = F32ToBf16(e_even, e_odd);
        return F32ToBf16(op_even, op_odd);
    }

    template <> EIGEN_STRONG_INLINE Packet8bf psin<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(psin_float, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pcos<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pcos_float, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf plog<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(plog_float, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pfloor<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pfloor<Packet4f>, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pceil<Packet4f>, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(pround<Packet4f>, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf>(const Packet8bf& a) { BF16_TO_F32_UNARY_OP_WRAPPER(print<Packet4f>, a); }
    template <> EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c)
    {
        Packet4f a_even = Bf16ToF32Even(a);
        Packet4f a_odd = Bf16ToF32Odd(a);
        Packet4f b_even = Bf16ToF32Even(b);
        Packet4f b_odd = Bf16ToF32Odd(b);
        Packet4f c_even = Bf16ToF32Even(c);
        Packet4f c_odd = Bf16ToF32Odd(c);
        Packet4f pmadd_even = pmadd<Packet4f>(a_even, b_even, c_even);
        Packet4f pmadd_odd = pmadd<Packet4f>(a_odd, b_odd, c_odd);
        return F32ToBf16(pmadd_even, pmadd_odd);
    }

    template <> EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(pmin<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf pmax<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER(pmax<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE Packet8bf pcmp_lt(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt<Packet4f>, a, b); }
    template <> EIGEN_STRONG_INLINE Packet8bf pcmp_lt_or_nan(const Packet8bf& a, const Packet8bf& b)
    {
        BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt_or_nan<Packet4f>, a, b);
    }
    template <> EIGEN_STRONG_INLINE Packet8bf pcmp_le(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_le<Packet4f>, a, b); }
    template <> EIGEN_STRONG_INLINE Packet8bf pcmp_eq(const Packet8bf& a, const Packet8bf& b) { BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_eq<Packet4f>, a, b); }

    template <> EIGEN_STRONG_INLINE bfloat16 pfirst(const Packet8bf& a) { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16((pfirst<Packet8us>(a))); }

    template <> EIGEN_STRONG_INLINE Packet8bf ploaddup<Packet8bf>(const bfloat16* from)
    {
        return ploaddup<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
    }

    template <> EIGEN_STRONG_INLINE Packet8bf plset<Packet8bf>(const bfloat16& a)
    {
        bfloat16 countdown[8] = {bfloat16(0), bfloat16(1), bfloat16(2), bfloat16(3), bfloat16(4), bfloat16(5), bfloat16(6), bfloat16(7)};
        return padd<Packet8bf>(pset1<Packet8bf>(a), pload<Packet8bf>(countdown));
    }

    template <> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
    {
        Packet4f b, sum;
        b = vec_sld(a, a, 8);
        sum = a + b;
        b = vec_sld(sum, sum, 4);
        sum += b;
        return pfirst(sum);
    }

    template <> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
    {
        Packet4i sum;
        sum = vec_sums(a, p4i_ZERO);
#ifdef _BIG_ENDIAN
        sum = vec_sld(sum, p4i_ZERO, 12);
#else
        sum = vec_sld(p4i_ZERO, sum, 4);
#endif
        return pfirst(sum);
    }

    template <> EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a)
    {
        float redux_even = predux<Packet4f>(Bf16ToF32Even(a));
        float redux_odd = predux<Packet4f>(Bf16ToF32Odd(a));
        float f32_result = redux_even + redux_odd;
        return bfloat16(f32_result);
    }
    template <typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size8(const Packet& a)
    {
        union
        {
            Packet v;
            __UNPACK_TYPE__(Packet) n[8];
        } vt;
        vt.v = a;

        EIGEN_ALIGN16 int first_loader[4] = {vt.n[0], vt.n[1], vt.n[2], vt.n[3]};
        EIGEN_ALIGN16 int second_loader[4] = {vt.n[4], vt.n[5], vt.n[6], vt.n[7]};
        Packet4i first_half = pload<Packet4i>(first_loader);
        Packet4i second_half = pload<Packet4i>(second_loader);

        return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_half) + predux(second_half));
    }

    template <> EIGEN_STRONG_INLINE short int predux<Packet8s>(const Packet8s& a) { return predux_size8<Packet8s>(a); }

    template <> EIGEN_STRONG_INLINE unsigned short int predux<Packet8us>(const Packet8us& a) { return predux_size8<Packet8us>(a); }

    template <typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size16(const Packet& a)
    {
        union
        {
            Packet v;
            __UNPACK_TYPE__(Packet) n[16];
        } vt;
        vt.v = a;

        EIGEN_ALIGN16 int first_loader[4] = {vt.n[0], vt.n[1], vt.n[2], vt.n[3]};
        EIGEN_ALIGN16 int second_loader[4] = {vt.n[4], vt.n[5], vt.n[6], vt.n[7]};
        EIGEN_ALIGN16 int third_loader[4] = {vt.n[8], vt.n[9], vt.n[10], vt.n[11]};
        EIGEN_ALIGN16 int fourth_loader[4] = {vt.n[12], vt.n[13], vt.n[14], vt.n[15]};

        Packet4i first_quarter = pload<Packet4i>(first_loader);
        Packet4i second_quarter = pload<Packet4i>(second_loader);
        Packet4i third_quarter = pload<Packet4i>(third_loader);
        Packet4i fourth_quarter = pload<Packet4i>(fourth_loader);

        return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_quarter) + predux(second_quarter) + predux(third_quarter) + predux(fourth_quarter));
    }

    template <> EIGEN_STRONG_INLINE signed char predux<Packet16c>(const Packet16c& a) { return predux_size16<Packet16c>(a); }

    template <> EIGEN_STRONG_INLINE unsigned char predux<Packet16uc>(const Packet16uc& a) { return predux_size16<Packet16uc>(a); }

    // Other reduction functions:
    // mul
    template <> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
    {
        Packet4f prod;
        prod = pmul(a, vec_sld(a, a, 8));
        return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
    }

    template <> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
    {
        EIGEN_ALIGN16 int aux[4];
        pstore(aux, a);
        return aux[0] * aux[1] * aux[2] * aux[3];
    }

    template <> EIGEN_STRONG_INLINE short int predux_mul<Packet8s>(const Packet8s& a)
    {
        Packet8s pair, quad, octo;

        pair = vec_mul(a, vec_sld(a, a, 8));
        quad = vec_mul(pair, vec_sld(pair, pair, 4));
        octo = vec_mul(quad, vec_sld(quad, quad, 2));

        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE unsigned short int predux_mul<Packet8us>(const Packet8us& a)
    {
        Packet8us pair, quad, octo;

        pair = vec_mul(a, vec_sld(a, a, 8));
        quad = vec_mul(pair, vec_sld(pair, pair, 4));
        octo = vec_mul(quad, vec_sld(quad, quad, 2));

        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a)
    {
        float redux_even = predux_mul<Packet4f>(Bf16ToF32Even(a));
        float redux_odd = predux_mul<Packet4f>(Bf16ToF32Odd(a));
        float f32_result = redux_even * redux_odd;
        return bfloat16(f32_result);
    }

    template <> EIGEN_STRONG_INLINE signed char predux_mul<Packet16c>(const Packet16c& a)
    {
        Packet16c pair, quad, octo, result;

        pair = vec_mul(a, vec_sld(a, a, 8));
        quad = vec_mul(pair, vec_sld(pair, pair, 4));
        octo = vec_mul(quad, vec_sld(quad, quad, 2));
        result = vec_mul(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }

    template <> EIGEN_STRONG_INLINE unsigned char predux_mul<Packet16uc>(const Packet16uc& a)
    {
        Packet16uc pair, quad, octo, result;

        pair = vec_mul(a, vec_sld(a, a, 8));
        quad = vec_mul(pair, vec_sld(pair, pair, 4));
        octo = vec_mul(quad, vec_sld(quad, quad, 2));
        result = vec_mul(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }

    // min
    template <typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_min4(const Packet& a)
    {
        Packet b, res;
        b = vec_min(a, vec_sld(a, a, 8));
        res = vec_min(b, vec_sld(b, b, 4));
        return pfirst(res);
    }

    template <> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) { return predux_min4<Packet4f>(a); }

    template <> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a) { return predux_min4<Packet4i>(a); }

    template <> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a)
    {
        float redux_even = predux_min<Packet4f>(Bf16ToF32Even(a));
        float redux_odd = predux_min<Packet4f>(Bf16ToF32Odd(a));
        float f32_result = (std::min)(redux_even, redux_odd);
        return bfloat16(f32_result);
    }

    template <> EIGEN_STRONG_INLINE short int predux_min<Packet8s>(const Packet8s& a)
    {
        Packet8s pair, quad, octo;

        //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
        pair = vec_min(a, vec_sld(a, a, 8));

        //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
        quad = vec_min(pair, vec_sld(pair, pair, 4));

        //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
        octo = vec_min(quad, vec_sld(quad, quad, 2));
        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE unsigned short int predux_min<Packet8us>(const Packet8us& a)
    {
        Packet8us pair, quad, octo;

        //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
        pair = vec_min(a, vec_sld(a, a, 8));

        //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
        quad = vec_min(pair, vec_sld(pair, pair, 4));

        //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
        octo = vec_min(quad, vec_sld(quad, quad, 2));
        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE signed char predux_min<Packet16c>(const Packet16c& a)
    {
        Packet16c pair, quad, octo, result;

        pair = vec_min(a, vec_sld(a, a, 8));
        quad = vec_min(pair, vec_sld(pair, pair, 4));
        octo = vec_min(quad, vec_sld(quad, quad, 2));
        result = vec_min(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }

    template <> EIGEN_STRONG_INLINE unsigned char predux_min<Packet16uc>(const Packet16uc& a)
    {
        Packet16uc pair, quad, octo, result;

        pair = vec_min(a, vec_sld(a, a, 8));
        quad = vec_min(pair, vec_sld(pair, pair, 4));
        octo = vec_min(quad, vec_sld(quad, quad, 2));
        result = vec_min(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }
    // max
    template <typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_max4(const Packet& a)
    {
        Packet b, res;
        b = vec_max(a, vec_sld(a, a, 8));
        res = vec_max(b, vec_sld(b, b, 4));
        return pfirst(res);
    }

    template <> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) { return predux_max4<Packet4f>(a); }

    template <> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a) { return predux_max4<Packet4i>(a); }

    template <> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a)
    {
        float redux_even = predux_max<Packet4f>(Bf16ToF32Even(a));
        float redux_odd = predux_max<Packet4f>(Bf16ToF32Odd(a));
        float f32_result = (std::max)(redux_even, redux_odd);
        return bfloat16(f32_result);
    }

    template <> EIGEN_STRONG_INLINE short int predux_max<Packet8s>(const Packet8s& a)
    {
        Packet8s pair, quad, octo;

        //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
        pair = vec_max(a, vec_sld(a, a, 8));

        //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
        quad = vec_max(pair, vec_sld(pair, pair, 4));

        //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
        octo = vec_max(quad, vec_sld(quad, quad, 2));
        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE unsigned short int predux_max<Packet8us>(const Packet8us& a)
    {
        Packet8us pair, quad, octo;

        //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
        pair = vec_max(a, vec_sld(a, a, 8));

        //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
        quad = vec_max(pair, vec_sld(pair, pair, 4));

        //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
        octo = vec_max(quad, vec_sld(quad, quad, 2));
        return pfirst(octo);
    }

    template <> EIGEN_STRONG_INLINE signed char predux_max<Packet16c>(const Packet16c& a)
    {
        Packet16c pair, quad, octo, result;

        pair = vec_max(a, vec_sld(a, a, 8));
        quad = vec_max(pair, vec_sld(pair, pair, 4));
        octo = vec_max(quad, vec_sld(quad, quad, 2));
        result = vec_max(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }

    template <> EIGEN_STRONG_INLINE unsigned char predux_max<Packet16uc>(const Packet16uc& a)
    {
        Packet16uc pair, quad, octo, result;

        pair = vec_max(a, vec_sld(a, a, 8));
        quad = vec_max(pair, vec_sld(pair, pair, 4));
        octo = vec_max(quad, vec_sld(quad, quad, 2));
        result = vec_max(octo, vec_sld(octo, octo, 1));

        return pfirst(result);
    }

    template <> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x) { return vec_any_ne(x, pzero(x)); }

    template <typename T> EIGEN_DEVICE_FUNC inline void ptranpose_common(PacketBlock<T, 4>& kernel)
    {
        T t0, t1, t2, t3;
        t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
        t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
        t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
        t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f, 4>& kernel) { ptranpose_common<Packet4f>(kernel); }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4i, 4>& kernel) { ptranpose_common<Packet4i>(kernel); }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8s, 4>& kernel)
    {
        Packet8s t0, t1, t2, t3;
        t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
        t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
        t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
        t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8us, 4>& kernel)
    {
        Packet8us t0, t1, t2, t3;
        t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
        t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
        t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
        t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8bf, 4>& kernel)
    {
        Packet8us t0, t1, t2, t3;

        t0 = vec_mergeh(kernel.packet[0].m_val, kernel.packet[2].m_val);
        t1 = vec_mergel(kernel.packet[0].m_val, kernel.packet[2].m_val);
        t2 = vec_mergeh(kernel.packet[1].m_val, kernel.packet[3].m_val);
        t3 = vec_mergel(kernel.packet[1].m_val, kernel.packet[3].m_val);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16c, 4>& kernel)
    {
        Packet16c t0, t1, t2, t3;
        t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
        t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
        t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
        t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16uc, 4>& kernel)
    {
        Packet16uc t0, t1, t2, t3;
        t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
        t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
        t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
        t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
        kernel.packet[0] = vec_mergeh(t0, t2);
        kernel.packet[1] = vec_mergel(t0, t2);
        kernel.packet[2] = vec_mergeh(t1, t3);
        kernel.packet[3] = vec_mergel(t1, t3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8s, 8>& kernel)
    {
        Packet8s v[8], sum[8];

        v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
        v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
        v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
        v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
        v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
        v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
        v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
        v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
        sum[0] = vec_mergeh(v[0], v[4]);
        sum[1] = vec_mergel(v[0], v[4]);
        sum[2] = vec_mergeh(v[1], v[5]);
        sum[3] = vec_mergel(v[1], v[5]);
        sum[4] = vec_mergeh(v[2], v[6]);
        sum[5] = vec_mergel(v[2], v[6]);
        sum[6] = vec_mergeh(v[3], v[7]);
        sum[7] = vec_mergel(v[3], v[7]);

        kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
        kernel.packet[1] = vec_mergel(sum[0], sum[4]);
        kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
        kernel.packet[3] = vec_mergel(sum[1], sum[5]);
        kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
        kernel.packet[5] = vec_mergel(sum[2], sum[6]);
        kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
        kernel.packet[7] = vec_mergel(sum[3], sum[7]);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8us, 8>& kernel)
    {
        Packet8us v[8], sum[8];

        v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
        v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
        v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
        v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
        v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
        v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
        v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
        v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
        sum[0] = vec_mergeh(v[0], v[4]);
        sum[1] = vec_mergel(v[0], v[4]);
        sum[2] = vec_mergeh(v[1], v[5]);
        sum[3] = vec_mergel(v[1], v[5]);
        sum[4] = vec_mergeh(v[2], v[6]);
        sum[5] = vec_mergel(v[2], v[6]);
        sum[6] = vec_mergeh(v[3], v[7]);
        sum[7] = vec_mergel(v[3], v[7]);

        kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
        kernel.packet[1] = vec_mergel(sum[0], sum[4]);
        kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
        kernel.packet[3] = vec_mergel(sum[1], sum[5]);
        kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
        kernel.packet[5] = vec_mergel(sum[2], sum[6]);
        kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
        kernel.packet[7] = vec_mergel(sum[3], sum[7]);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8bf, 8>& kernel)
    {
        Packet8bf v[8], sum[8];

        v[0] = vec_mergeh(kernel.packet[0].m_val, kernel.packet[4].m_val);
        v[1] = vec_mergel(kernel.packet[0].m_val, kernel.packet[4].m_val);
        v[2] = vec_mergeh(kernel.packet[1].m_val, kernel.packet[5].m_val);
        v[3] = vec_mergel(kernel.packet[1].m_val, kernel.packet[5].m_val);
        v[4] = vec_mergeh(kernel.packet[2].m_val, kernel.packet[6].m_val);
        v[5] = vec_mergel(kernel.packet[2].m_val, kernel.packet[6].m_val);
        v[6] = vec_mergeh(kernel.packet[3].m_val, kernel.packet[7].m_val);
        v[7] = vec_mergel(kernel.packet[3].m_val, kernel.packet[7].m_val);
        sum[0] = vec_mergeh(v[0].m_val, v[4].m_val);
        sum[1] = vec_mergel(v[0].m_val, v[4].m_val);
        sum[2] = vec_mergeh(v[1].m_val, v[5].m_val);
        sum[3] = vec_mergel(v[1].m_val, v[5].m_val);
        sum[4] = vec_mergeh(v[2].m_val, v[6].m_val);
        sum[5] = vec_mergel(v[2].m_val, v[6].m_val);
        sum[6] = vec_mergeh(v[3].m_val, v[7].m_val);
        sum[7] = vec_mergel(v[3].m_val, v[7].m_val);

        kernel.packet[0] = vec_mergeh(sum[0].m_val, sum[4].m_val);
        kernel.packet[1] = vec_mergel(sum[0].m_val, sum[4].m_val);
        kernel.packet[2] = vec_mergeh(sum[1].m_val, sum[5].m_val);
        kernel.packet[3] = vec_mergel(sum[1].m_val, sum[5].m_val);
        kernel.packet[4] = vec_mergeh(sum[2].m_val, sum[6].m_val);
        kernel.packet[5] = vec_mergel(sum[2].m_val, sum[6].m_val);
        kernel.packet[6] = vec_mergeh(sum[3].m_val, sum[7].m_val);
        kernel.packet[7] = vec_mergel(sum[3].m_val, sum[7].m_val);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16c, 16>& kernel)
    {
        Packet16c step1[16], step2[16], step3[16];

        step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
        step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
        step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
        step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
        step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
        step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
        step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
        step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
        step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
        step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
        step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
        step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
        step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
        step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
        step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
        step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);

        step2[0] = vec_mergeh(step1[0], step1[8]);
        step2[1] = vec_mergel(step1[0], step1[8]);
        step2[2] = vec_mergeh(step1[1], step1[9]);
        step2[3] = vec_mergel(step1[1], step1[9]);
        step2[4] = vec_mergeh(step1[2], step1[10]);
        step2[5] = vec_mergel(step1[2], step1[10]);
        step2[6] = vec_mergeh(step1[3], step1[11]);
        step2[7] = vec_mergel(step1[3], step1[11]);
        step2[8] = vec_mergeh(step1[4], step1[12]);
        step2[9] = vec_mergel(step1[4], step1[12]);
        step2[10] = vec_mergeh(step1[5], step1[13]);
        step2[11] = vec_mergel(step1[5], step1[13]);
        step2[12] = vec_mergeh(step1[6], step1[14]);
        step2[13] = vec_mergel(step1[6], step1[14]);
        step2[14] = vec_mergeh(step1[7], step1[15]);
        step2[15] = vec_mergel(step1[7], step1[15]);

        step3[0] = vec_mergeh(step2[0], step2[8]);
        step3[1] = vec_mergel(step2[0], step2[8]);
        step3[2] = vec_mergeh(step2[1], step2[9]);
        step3[3] = vec_mergel(step2[1], step2[9]);
        step3[4] = vec_mergeh(step2[2], step2[10]);
        step3[5] = vec_mergel(step2[2], step2[10]);
        step3[6] = vec_mergeh(step2[3], step2[11]);
        step3[7] = vec_mergel(step2[3], step2[11]);
        step3[8] = vec_mergeh(step2[4], step2[12]);
        step3[9] = vec_mergel(step2[4], step2[12]);
        step3[10] = vec_mergeh(step2[5], step2[13]);
        step3[11] = vec_mergel(step2[5], step2[13]);
        step3[12] = vec_mergeh(step2[6], step2[14]);
        step3[13] = vec_mergel(step2[6], step2[14]);
        step3[14] = vec_mergeh(step2[7], step2[15]);
        step3[15] = vec_mergel(step2[7], step2[15]);

        kernel.packet[0] = vec_mergeh(step3[0], step3[8]);
        kernel.packet[1] = vec_mergel(step3[0], step3[8]);
        kernel.packet[2] = vec_mergeh(step3[1], step3[9]);
        kernel.packet[3] = vec_mergel(step3[1], step3[9]);
        kernel.packet[4] = vec_mergeh(step3[2], step3[10]);
        kernel.packet[5] = vec_mergel(step3[2], step3[10]);
        kernel.packet[6] = vec_mergeh(step3[3], step3[11]);
        kernel.packet[7] = vec_mergel(step3[3], step3[11]);
        kernel.packet[8] = vec_mergeh(step3[4], step3[12]);
        kernel.packet[9] = vec_mergel(step3[4], step3[12]);
        kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
        kernel.packet[11] = vec_mergel(step3[5], step3[13]);
        kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
        kernel.packet[13] = vec_mergel(step3[6], step3[14]);
        kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
        kernel.packet[15] = vec_mergel(step3[7], step3[15]);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16uc, 16>& kernel)
    {
        Packet16uc step1[16], step2[16], step3[16];

        step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
        step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
        step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
        step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
        step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
        step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
        step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
        step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
        step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
        step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
        step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
        step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
        step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
        step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
        step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
        step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);

        step2[0] = vec_mergeh(step1[0], step1[8]);
        step2[1] = vec_mergel(step1[0], step1[8]);
        step2[2] = vec_mergeh(step1[1], step1[9]);
        step2[3] = vec_mergel(step1[1], step1[9]);
        step2[4] = vec_mergeh(step1[2], step1[10]);
        step2[5] = vec_mergel(step1[2], step1[10]);
        step2[6] = vec_mergeh(step1[3], step1[11]);
        step2[7] = vec_mergel(step1[3], step1[11]);
        step2[8] = vec_mergeh(step1[4], step1[12]);
        step2[9] = vec_mergel(step1[4], step1[12]);
        step2[10] = vec_mergeh(step1[5], step1[13]);
        step2[11] = vec_mergel(step1[5], step1[13]);
        step2[12] = vec_mergeh(step1[6], step1[14]);
        step2[13] = vec_mergel(step1[6], step1[14]);
        step2[14] = vec_mergeh(step1[7], step1[15]);
        step2[15] = vec_mergel(step1[7], step1[15]);

        step3[0] = vec_mergeh(step2[0], step2[8]);
        step3[1] = vec_mergel(step2[0], step2[8]);
        step3[2] = vec_mergeh(step2[1], step2[9]);
        step3[3] = vec_mergel(step2[1], step2[9]);
        step3[4] = vec_mergeh(step2[2], step2[10]);
        step3[5] = vec_mergel(step2[2], step2[10]);
        step3[6] = vec_mergeh(step2[3], step2[11]);
        step3[7] = vec_mergel(step2[3], step2[11]);
        step3[8] = vec_mergeh(step2[4], step2[12]);
        step3[9] = vec_mergel(step2[4], step2[12]);
        step3[10] = vec_mergeh(step2[5], step2[13]);
        step3[11] = vec_mergel(step2[5], step2[13]);
        step3[12] = vec_mergeh(step2[6], step2[14]);
        step3[13] = vec_mergel(step2[6], step2[14]);
        step3[14] = vec_mergeh(step2[7], step2[15]);
        step3[15] = vec_mergel(step2[7], step2[15]);

        kernel.packet[0] = vec_mergeh(step3[0], step3[8]);
        kernel.packet[1] = vec_mergel(step3[0], step3[8]);
        kernel.packet[2] = vec_mergeh(step3[1], step3[9]);
        kernel.packet[3] = vec_mergel(step3[1], step3[9]);
        kernel.packet[4] = vec_mergeh(step3[2], step3[10]);
        kernel.packet[5] = vec_mergel(step3[2], step3[10]);
        kernel.packet[6] = vec_mergeh(step3[3], step3[11]);
        kernel.packet[7] = vec_mergel(step3[3], step3[11]);
        kernel.packet[8] = vec_mergeh(step3[4], step3[12]);
        kernel.packet[9] = vec_mergel(step3[4], step3[12]);
        kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
        kernel.packet[11] = vec_mergel(step3[5], step3[13]);
        kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
        kernel.packet[13] = vec_mergel(step3[6], step3[14]);
        kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
        kernel.packet[15] = vec_mergel(step3[7], step3[15]);
    }

    template <typename Packet> EIGEN_STRONG_INLINE Packet pblend4(const Selector<4>& ifPacket, const Packet& thenPacket, const Packet& elsePacket)
    {
        Packet4ui select = {ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3]};
        Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
        return vec_sel(elsePacket, thenPacket, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket)
    {
        return pblend4<Packet4i>(ifPacket, thenPacket, elsePacket);
    }

    template <> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket)
    {
        return pblend4<Packet4f>(ifPacket, thenPacket, elsePacket);
    }

    template <> EIGEN_STRONG_INLINE Packet8s pblend(const Selector<8>& ifPacket, const Packet8s& thenPacket, const Packet8s& elsePacket)
    {
        Packet8us select = {ifPacket.select[0],
                            ifPacket.select[1],
                            ifPacket.select[2],
                            ifPacket.select[3],
                            ifPacket.select[4],
                            ifPacket.select[5],
                            ifPacket.select[6],
                            ifPacket.select[7]};
        Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(select, p8us_ONE));
        Packet8s result = vec_sel(elsePacket, thenPacket, mask);
        return result;
    }

    template <> EIGEN_STRONG_INLINE Packet8us pblend(const Selector<8>& ifPacket, const Packet8us& thenPacket, const Packet8us& elsePacket)
    {
        Packet8us select = {ifPacket.select[0],
                            ifPacket.select[1],
                            ifPacket.select[2],
                            ifPacket.select[3],
                            ifPacket.select[4],
                            ifPacket.select[5],
                            ifPacket.select[6],
                            ifPacket.select[7]};
        Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(reinterpret_cast<Packet8us>(select), p8us_ONE));
        return vec_sel(elsePacket, thenPacket, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet8bf pblend(const Selector<8>& ifPacket, const Packet8bf& thenPacket, const Packet8bf& elsePacket)
    {
        return pblend<Packet8us>(ifPacket, thenPacket, elsePacket);
    }

    template <> EIGEN_STRONG_INLINE Packet16c pblend(const Selector<16>& ifPacket, const Packet16c& thenPacket, const Packet16c& elsePacket)
    {
        Packet16uc select = {ifPacket.select[0],
                             ifPacket.select[1],
                             ifPacket.select[2],
                             ifPacket.select[3],
                             ifPacket.select[4],
                             ifPacket.select[5],
                             ifPacket.select[6],
                             ifPacket.select[7],
                             ifPacket.select[8],
                             ifPacket.select[9],
                             ifPacket.select[10],
                             ifPacket.select[11],
                             ifPacket.select[12],
                             ifPacket.select[13],
                             ifPacket.select[14],
                             ifPacket.select[15]};

        Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
        return vec_sel(elsePacket, thenPacket, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet16uc pblend(const Selector<16>& ifPacket, const Packet16uc& thenPacket, const Packet16uc& elsePacket)
    {
        Packet16uc select = {ifPacket.select[0],
                             ifPacket.select[1],
                             ifPacket.select[2],
                             ifPacket.select[3],
                             ifPacket.select[4],
                             ifPacket.select[5],
                             ifPacket.select[6],
                             ifPacket.select[7],
                             ifPacket.select[8],
                             ifPacket.select[9],
                             ifPacket.select[10],
                             ifPacket.select[11],
                             ifPacket.select[12],
                             ifPacket.select[13],
                             ifPacket.select[14],
                             ifPacket.select[15]};

        Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
        return vec_sel(elsePacket, thenPacket, mask);
    }

    template <> struct type_casting_traits<float, int>
    {
        enum
        {
            VectorizedCast = 1,
            SrcCoeffRatio = 1,
            TgtCoeffRatio = 1
        };
    };

    template <> struct type_casting_traits<int, float>
    {
        enum
        {
            VectorizedCast = 1,
            SrcCoeffRatio = 1,
            TgtCoeffRatio = 1
        };
    };

    template <> struct type_casting_traits<bfloat16, unsigned short int>
    {
        enum
        {
            VectorizedCast = 1,
            SrcCoeffRatio = 1,
            TgtCoeffRatio = 1
        };
    };

    template <> struct type_casting_traits<unsigned short int, bfloat16>
    {
        enum
        {
            VectorizedCast = 1,
            SrcCoeffRatio = 1,
            TgtCoeffRatio = 1
        };
    };

    template <> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) { return vec_cts(a, 0); }

    template <> EIGEN_STRONG_INLINE Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) { return vec_ctu(a, 0); }

    template <> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) { return vec_ctf(a, 0); }

    template <> EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) { return vec_ctf(a, 0); }

    template <> EIGEN_STRONG_INLINE Packet8us pcast<Packet8bf, Packet8us>(const Packet8bf& a)
    {
        Packet4f float_even = Bf16ToF32Even(a);
        Packet4f float_odd = Bf16ToF32Odd(a);
        Packet4ui int_even = pcast<Packet4f, Packet4ui>(float_even);
        Packet4ui int_odd = pcast<Packet4f, Packet4ui>(float_odd);
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
        Packet4ui low_even = pand<Packet4ui>(int_even, p4ui_low_mask);
        Packet4ui low_odd = pand<Packet4ui>(int_odd, p4ui_low_mask);

        //Check values that are bigger than USHRT_MAX (0xFFFF)
        Packet4bi overflow_selector;
        if (vec_any_gt(int_even, p4ui_low_mask))
        {
            overflow_selector = vec_cmpgt(int_even, p4ui_low_mask);
            low_even = vec_sel(low_even, p4ui_low_mask, overflow_selector);
        }
        if (vec_any_gt(int_odd, p4ui_low_mask))
        {
            overflow_selector = vec_cmpgt(int_odd, p4ui_low_mask);
            low_odd = vec_sel(low_even, p4ui_low_mask, overflow_selector);
        }

        low_odd = plogical_shift_left<16>(low_odd);

        Packet4ui int_final = por<Packet4ui>(low_even, low_odd);
        return reinterpret_cast<Packet8us>(int_final);
    }

    template <> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8us, Packet8bf>(const Packet8us& a)
    {
        //short -> int -> float -> bfloat16
        const _EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
        Packet4ui int_cast = reinterpret_cast<Packet4ui>(a);
        Packet4ui int_even = pand<Packet4ui>(int_cast, p4ui_low_mask);
        Packet4ui int_odd = plogical_shift_right<16>(int_cast);
        Packet4f float_even = pcast<Packet4ui, Packet4f>(int_even);
        Packet4f float_odd = pcast<Packet4ui, Packet4f>(int_odd);
        return F32ToBf16(float_even, float_odd);
    }

    template <> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet4f>(const Packet4f& a) { return reinterpret_cast<Packet4i>(a); }

    template <> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet4i>(const Packet4i& a) { return reinterpret_cast<Packet4f>(a); }

//---------- double ----------
#ifdef __VSX__
    typedef __vector double Packet2d;
    typedef __vector unsigned long long Packet2ul;
    typedef __vector long long Packet2l;
#if EIGEN_COMP_CLANG
    typedef Packet2ul Packet2bl;
#else
    typedef __vector __bool long Packet2bl;
#endif

    static Packet2l p2l_ONE = {1, 1};
    static Packet2l p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
    static Packet2ul p2ul_SIGN = {0x8000000000000000ull, 0x8000000000000000ull};
    static Packet2ul p2ul_PREV0DOT5 = {0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull};
    static Packet2d p2d_ONE = {1.0, 1.0};
    static Packet2d p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);
    static Packet2d p2d_MZERO = {numext::bit_cast<double>(0x8000000000000000ull), numext::bit_cast<double>(0x8000000000000000ull)};

#ifdef _BIG_ENDIAN
    static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8));
#else
    static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));
#endif

    template <int index> Packet2d vec_splat_dbl(Packet2d& a) { return vec_splat(a, index); }

    template <> struct packet_traits<double> : default_packet_traits
    {
        typedef Packet2d type;
        typedef Packet2d half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 2,
            HasHalfPacket = 1,

            HasAdd = 1,
            HasSub = 1,
            HasMul = 1,
            HasDiv = 1,
            HasMin = 1,
            HasMax = 1,
            HasAbs = 1,
            HasSin = 0,
            HasCos = 0,
            HasLog = 0,
            HasExp = 1,
            HasSqrt = 1,
            HasRsqrt = 1,
            HasRound = 1,
            HasFloor = 1,
            HasCeil = 1,
            HasRint = 1,
            HasNegate = 1,
            HasBlend = 1
        };
    };

    template <> struct unpacket_traits<Packet2d>
    {
        typedef double type;
        enum
        {
            size = 2,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
        typedef Packet2d half;
    };

    inline std::ostream& operator<<(std::ostream& s, const Packet2l& v)
    {
        union
        {
            Packet2l v;
            int64_t n[2];
        } vt;
        vt.v = v;
        s << vt.n[0] << ", " << vt.n[1];
        return s;
    }

    inline std::ostream& operator<<(std::ostream& s, const Packet2d& v)
    {
        union
        {
            Packet2d v;
            double n[2];
        } vt;
        vt.v = v;
        s << vt.n[0] << ", " << vt.n[1];
        return s;
    }

    // Need to define them first or we get specialization after instantiation errors
    template <> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
    {
        EIGEN_DEBUG_ALIGNED_LOAD
        return vec_xl(0, const_cast<double*>(from));  // cast needed by Clang
    }

    template <> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from)
    {
        EIGEN_DEBUG_ALIGNED_STORE
        vec_xst(from, 0, to);
    }

    template <> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from)
    {
        Packet2d v = {from, from};
        return v;
    }

    template <> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(unsigned long from)
    {
        Packet2l v = {static_cast<long long>(from), static_cast<long long>(from)};
        return reinterpret_cast<Packet2d>(v);
    }

    template <> EIGEN_STRONG_INLINE void pbroadcast4<Packet2d>(const double* a, Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
    {
        //This way is faster than vec_splat (at least for doubles in Power 9)
        a0 = pset1<Packet2d>(a[0]);
        a1 = pset1<Packet2d>(a[1]);
        a2 = pset1<Packet2d>(a[2]);
        a3 = pset1<Packet2d>(a[3]);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
    {
        EIGEN_ALIGN16 double af[2];
        af[0] = from[0 * stride];
        af[1] = from[1 * stride];
        return pload<Packet2d>(af);
    }
    template <> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
    {
        EIGEN_ALIGN16 double af[2];
        pstore<double>(af, from);
        to[0 * stride] = af[0];
        to[1 * stride] = af[1];
    }

    template <> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; }

    template <> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; }

    template <> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; }

    template <> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; }

    template <> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }

    template <> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_madd(a, b, p2d_MZERO); }
    template <> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_div(a, b); }

    // for some weird raisons, it has to be overloaded for packet of integers
    template <> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }

    template <> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
        Packet2d ret;
        __asm__("xvcmpgedp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa"(ret) : "wa"(a), "wa"(b));
        return ret;
    }

    template <> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
        Packet2d ret;
        __asm__("xvcmpgtdp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa"(ret) : "wa"(a), "wa"(b));
        return ret;
    }

    template <> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmple(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmplt(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmpeq(a, b)); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b)
    {
        Packet2d c = reinterpret_cast<Packet2d>(vec_cmpge(a, b));
        return vec_nor(c, c);
    }

    template <> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }

    template <> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }

    template <> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }

    template <> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }

    template <> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a)
    {
        Packet2d t = vec_add(reinterpret_cast<Packet2d>(vec_or(vec_and(reinterpret_cast<Packet2ul>(a), p2ul_SIGN), p2ul_PREV0DOT5)), a);
        Packet2d res;

        __asm__("xvrdpiz %x0, %x1\n\t" : "=&wa"(res) : "wa"(t));

        return res;
    }
    template <> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return vec_ceil(a); }
    template <> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
    template <> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a)
    {
        Packet2d res;

        __asm__("xvrdpic %x0, %x1\n\t" : "=&wa"(res) : "wa"(a));

        return res;
    }

    template <> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
        return vec_xl(0, const_cast<double*>(from));
    }

    template <> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
    {
        Packet2d p;
        if ((std::ptrdiff_t(from) % 16) == 0)
            p = pload<Packet2d>(from);
        else
            p = ploadu<Packet2d>(from);
        return vec_splat_dbl<0>(p);
    }

    template <> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from)
    {
        EIGEN_DEBUG_UNALIGNED_STORE
        vec_xst(from, 0, to);
    }

    template <> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }

    template <> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a)
    {
        EIGEN_ALIGN16 double x[2];
        pstore<double>(x, a);
        return x[0];
    }

    template <> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
    {
        return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
    }
    template <> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }

    // VSX support varies between different compilers and even different
    // versions of the same compiler.  For gcc version >= 4.9.3, we can use
    // vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use
    // a slow version that works with older compilers.
    // Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
    // are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
    template <> inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x)
    {
#if EIGEN_GNUC_AT_LEAST(5, 4) || (EIGEN_GNUC_AT(6, 1) && __GNUC_PATCHLEVEL__ >= 1)
        return vec_cts(x, 0);  // TODO: check clang version.
#else
        double tmp[2];
        memcpy(tmp, &x, sizeof(tmp));
        Packet2l l = {static_cast<long long>(tmp[0]), static_cast<long long>(tmp[1])};
        return l;
#endif
    }

    template <> inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x)
    {
        unsigned long long tmp[2];
        memcpy(tmp, &x, sizeof(tmp));
        Packet2d d = {static_cast<double>(tmp[0]), static_cast<double>(tmp[1])};
        return d;
    }

// Packet2l shifts.
// For POWER8 we simply use vec_sr/l.
//
// Things are more complicated for POWER7. There is actually a
// vec_xxsxdi intrinsic but it is not supported by some gcc versions.
// So we need to shift by N % 32 and rearrage bytes.
#ifdef __POWER8_VECTOR__

    template <int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a)
    {
        const Packet2ul shift = {N, N};
        return vec_sl(a, shift);
    }

    template <int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a)
    {
        const Packet2ul shift = {N, N};
        return vec_sr(a, shift);
    }

#else

    // Shifts [A, B, C, D] to [B, 0, D, 0].
    // Used to implement left shifts for Packet2l.
    EIGEN_ALWAYS_INLINE Packet4i shift_even_left(const Packet4i& a)
    {
        static const Packet16uc perm = {0x14, 0x15, 0x16, 0x17, 0x00, 0x01, 0x02, 0x03, 0x1c, 0x1d, 0x1e, 0x1f, 0x08, 0x09, 0x0a, 0x0b};
#ifdef _BIG_ENDIAN
        return vec_perm(p4i_ZERO, a, perm);
#else
        return vec_perm(a, p4i_ZERO, perm);
#endif
    }

    // Shifts [A, B, C, D] to [0, A, 0, C].
    // Used to implement right shifts for Packet2l.
    EIGEN_ALWAYS_INLINE Packet4i shift_odd_right(const Packet4i& a)
    {
        static const Packet16uc perm = {0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b};
#ifdef _BIG_ENDIAN
        return vec_perm(p4i_ZERO, a, perm);
#else
        return vec_perm(a, p4i_ZERO, perm);
#endif
    }

    template <int N, typename EnableIf = void> struct plogical_shift_left_impl;

    template <int N> struct plogical_shift_left_impl<N, typename enable_if<(N < 32) && (N >= 0)>::type>
    {
        static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a)
        {
            static const unsigned n = static_cast<unsigned>(N);
            const Packet4ui shift = {n, n, n, n};
            const Packet4i ai = reinterpret_cast<Packet4i>(a);
            static const unsigned m = static_cast<unsigned>(32 - N);
            const Packet4ui shift_right = {m, m, m, m};
            const Packet4i out_hi = vec_sl(ai, shift);
            const Packet4i out_lo = shift_even_left(vec_sr(ai, shift_right));
            return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
        }
    };

    template <int N> struct plogical_shift_left_impl<N, typename enable_if<(N >= 32)>::type>
    {
        static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a)
        {
            static const unsigned m = static_cast<unsigned>(N - 32);
            const Packet4ui shift = {m, m, m, m};
            const Packet4i ai = reinterpret_cast<Packet4i>(a);
            return reinterpret_cast<Packet2l>(shift_even_left(vec_sl(ai, shift)));
        }
    };

    template <int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) { return plogical_shift_left_impl<N>::run(a); }

    template <int N, typename EnableIf = void> struct plogical_shift_right_impl;

    template <int N> struct plogical_shift_right_impl<N, typename enable_if<(N < 32) && (N >= 0)>::type>
    {
        static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a)
        {
            static const unsigned n = static_cast<unsigned>(N);
            const Packet4ui shift = {n, n, n, n};
            const Packet4i ai = reinterpret_cast<Packet4i>(a);
            static const unsigned m = static_cast<unsigned>(32 - N);
            const Packet4ui shift_left = {m, m, m, m};
            const Packet4i out_lo = vec_sr(ai, shift);
            const Packet4i out_hi = shift_odd_right(vec_sl(ai, shift_left));
            return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
        }
    };

    template <int N> struct plogical_shift_right_impl<N, typename enable_if<(N >= 32)>::type>
    {
        static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a)
        {
            static const unsigned m = static_cast<unsigned>(N - 32);
            const Packet4ui shift = {m, m, m, m};
            const Packet4i ai = reinterpret_cast<Packet4i>(a);
            return reinterpret_cast<Packet2l>(shift_odd_right(vec_sr(ai, shift)));
        }
    };

    template <int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) { return plogical_shift_right_impl<N>::run(a); }
#endif

    template <> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent)
    {
        // Clamp exponent to [-2099, 2099]
        const Packet2d max_exponent = pset1<Packet2d>(2099.0);
        const Packet2l e = pcast<Packet2d, Packet2l>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));

        // Split 2^e into four factors and multiply:
        const Packet2l bias = {1023, 1023};
        Packet2l b = plogical_shift_right<2>(e);  // floor(e/4)
        Packet2d c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias));
        Packet2d out = pmul(pmul(pmul(a, c), c), c);                        // a * 2^(3b)
        b = psub(psub(psub(e, b), b), b);                                   // e - 3b
        c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias));  // 2^(e - 3b)
        out = pmul(out, c);                                                 // a * 2^e
        return out;
    }

    // Extract exponent without existence of Packet2l.
    template <> EIGEN_STRONG_INLINE Packet2d pfrexp_generic_get_biased_exponent(const Packet2d& a)
    {
        return pcast<Packet2l, Packet2d>(plogical_shift_right<52>(reinterpret_cast<Packet2l>(pabs(a))));
    }

    template <> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent) { return pfrexp_generic(a, exponent); }

    template <> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
    {
        Packet2d b, sum;
        b = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));
        sum = a + b;
        return pfirst<Packet2d>(sum);
    }

    // Other reduction functions:
    // mul
    template <> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
    {
        return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    }

    // min
    template <> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
    {
        return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    }

    // max
    template <> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
    {
        return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2d, 2>& kernel)
    {
        Packet2d t0, t1;
        t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
        t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
        kernel.packet[0] = t0;
        kernel.packet[1] = t1;
    }

    template <> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket)
    {
        Packet2l select = {ifPacket.select[0], ifPacket.select[1]};
        Packet2bl mask = reinterpret_cast<Packet2bl>(vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)));
        return vec_sel(elsePacket, thenPacket, mask);
    }

#endif  // __VSX__
}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_PACKET_MATH_ALTIVEC_H
